[tex]( a^{2}-2a+1)+( b^{2}-2 b\sqrt{2}+2)+( c^{2}-2c \sqrt{3}+3)=0 \\ (a-1)^2+(b- \sqrt{2})^2+(c- \sqrt{3})^2=0 \\ a=1;b= \sqrt{2};c= \sqrt{3} [/tex]
deci triunghiul este dreptunghic cu catetele a=1;b=√2 si ipotenuza c=√3
A=[tex] \frac{ab}{2}= \frac{1* \sqrt{2} }{2}= \frac{ \sqrt{2} }{2} [/tex]
